Equilibrium strategies in a defined benefit pension plan game

Producción CientíficaWe study the optimal management of an aggregated overfunded pension plan of defined benefit type as a two-player noncooperative differential game. The model’s key fact is to consider the fund surplus as a strategic variable that makes the pension plan more attractive both for current and future participants. We let the worker participants to act collectively as a single player that claims a share of the surplus, and let the sponsoring firm act as the player that cares about the investment of the surplus fund assets. The union’s objective is to maximize the expected discounted utility of the extra benefits claimed. We solve this asymmetric game under two different assumptions on the preferences of the firm: in the first scenario, the firm aims to maximize expected discounted utility derived from fund surplus; while in the second scenario, the firm cares about minimizing the probability that the fund surplus reaches very low values.Este trabajo se ha hecho con ayuda de los proyectos del Ministerio de Economía Industria y Competitividad (Spain), ECO2017-86261-P , ECO2014-56384-P y MDM2014-0431, y de la Comunidad de Madrid MadEco-CM S2015/HUM-3444 y Comunidad de Castilla y León VA148G18

Intergenerational transfer institutions public education and public pensions.

In a world in which credit markets to finance investments in human capital are rare, the competitive equilibrium allocation generally cannot achieve either static or dynamic efficiency. When generations overlap, this inefficiency can be overcome by properly designed institutions. We study the working of two such institutions: Public Education and Public Pensions. We argue that, when established jointly, they implement an intergenerational dynamic game of taxes and transfers through which public education for the young and public pensions for the elderly support each other. Through the public financing of education, the young borrow from the middle age to invest in human capital. When employed, they pay back their debt by means of a social security tax on labor income. The proceedings of the latter are used to finance pension payments to the now elderly lenders. We also show that such intergenerational agreement can be supported as a sub game perfect equilibrium of, relatively straightforward, majority voting games. While the intertemporal allocation so obtained does not necessarily reach full dynamic efficiency it does so under certain restrictions and it always improves upon the laissez-faire allocation. We test the main predictions of our model by using micro and macro data from Spain. The results are surprisingly good.Intergenerational contract; Efficiency; Human capital; Political equilibria;

Individual choice of pension arrangement as a pension reform strategy

The paper examines social security (public pension) reforms in which the programme is partially shifted from a public unfunded basis to a private, prefunded, basis. It focuses on reforms where individuals have a choice in switching from public funded to private unfunded programmes (as in the Ñ£ontracting outÒ scheme in the UK), or where some individuals are forced to join the funded scheme, or reforms which combine both these options. The welfare consequences of such reform strategies are analysed both from an individual and a macroeconomic perspective. The paper also examines whether individuals respond Ѳationally' to the incentives inherent in such programmes.

Privatizing Social Security: A Political-Economy Approach

The aging of the population shakes the public finance of pay- as-you-go social security systems. We develop a political-economy framework in which this demographic change leads to the downsizing of the social security system, and, as a consequence, to the emergence of supplemental individual retirement programs. Allowing for a one-shot budget deficit, earmarked to accommodate the cost of the social security reforms, is shown to facilitate the political-economy transition from a national to a private pension system.

A defined benefit pension plan game with Brownian and Poisson jumps uncertainty

Producción CientíficaIn this paper, we study the optimal management of an aggregated pension fund of defined benefit type by means of a differential game with two players, the firm and the participants. We assume that the fund wealth is greater than the actuarial liability and then the manager builds a pension fund surplus. In order to contemplate sudden changes in the financial market, the surplus can be invested in a portfolio with a bond and several risky assets where the uncertainty comes from Brownian motions and Poisson processes. The aim of the participants is to maximize a utility of the extra benefits. The game is analyzed in three scenarios. In the first, the aim of the firm is to maximize a utility of the fund surplus, in the second, to minimize the probability that the fund surplus reaches a low level, and in the third, to minimize the expected time of reaching a benchmark surplus. An infinite horizon is considered, and the game is solved by means of the dynamic programming approach. The influence of the jumps of the financial market on the Nash equilibrium strategies and the fund surplus is studied by means of a numerical illustration

Equilibria with social security

We model pay-as-you-go (PAYG) social sucurity systems as the outcome of majority voting within a standard OLG model with production and an exogenous population growth rateo At each point in time individuals work, save, consume and invest by taking the social security policy as given. The latter consists of a tax on current wages transferred to elderly people. When they vote, individuals have to make two choices: If they want to keep the committment made by the previous generation by paying the elderly the promised amount of benefits, and which amount they want paid to themselves next periodo We show that when the growth rate of population is high enough compared to the productivity of capital there exists an equilibrium where PAYG pensions are voted into existence and maintained. PAYG systems are kept even when everybody knows that they will surely be abondoned, and that some generation will pay and not be paid back. We characterize the steady state and dynamic properties of these equilibria and study their welfare properties. Equilibria achieved by voting are typically inefficient; however, they may be so due to overaccumulation, as well as, in other cases, due to under accumulation. On the other hand, the efficient steady states turn out to be dynamically unstable: so we are presenting an unpleasant alternative for policy making

Equilibria with social security.

We model pay-as-you-go (PAYG) social sucurity systems as the outcome of majority voting within a standard OLG model with production and an exogenous population growth rateo At each point in time individuals work, save, consume and invest by taking the social security policy as given. The latter consists of a tax on current wages transferred to elderly people. When they vote, individuals have to make two choices: If they want to keep the committment made by the previous generation by paying the elderly the promised amount of benefits, and which amount they want paid to themselves next periodo We show that when the growth rate of population is high enough compared to the productivity of capital there exists an equilibrium where PAYG pensions are voted into existence and maintained. PAYG systems are kept even when everybody knows that they will surely be abondoned, and that some generation will pay and not be paid back. We characterize the steady state and dynamic properties of these equilibria and study their welfare properties. Equilibria achieved by voting are typically inefficient; however, they may be so due to overaccumulation, as well as, in other cases, due to under accumulation. On the other hand, the efficient steady states turn out to be dynamically unstable: so we are presenting an unpleasant alternative for policy making.

Self-Control and Saving for Retirement

macroeconomics, Self-Control, Saving, Retirement

Intergenerational transfer institutions public education and public pensions

In a world in which credit markets to finance investments in human capital are rare, the competitive equilibrium allocation generally cannot achieve either static or dynamic efficiency. When generations overlap, this inefficiency can be overcome by properly designed institutions. We study the working of two such institutions: Public Education and Public Pensions. We argue that, when established jointly, they implement an intergenerational dynamic game of taxes and transfers through which public education for the young and public pensions for the elderly support each other. Through the public financing of education, the young borrow from the middle age to invest in human capital. When employed, they pay back their debt by means of a social security tax on labor income. The proceedings of the latter are used to finance pension payments to the now elderly lenders. We also show that such intergenerational agreement can be supported as a sub game perfect equilibrium of, relatively straightforward, majority voting games. While the intertemporal allocation so obtained does not necessarily reach full dynamic efficiency it does so under certain restrictions and it always improves upon the laissez-faire allocation. We test the main predictions of our model by using micro and macro data from Spain. The results are surprisingly good